Symbolism, Imagery, Allegory
The White Tree may be a sign of Gondor and the Seven Stones may be heirlooms of the house of Elendil, but the Seven Stars are the real symbols of Elendil's descendants. When Aragorn flies his banner in battle, Tolkien describes it:
There flowered a White Tree, and that was for Gondor; but Seven Stars were about it, and a high crown above it, the signs of Elendil that no lord had borne for years beyond count. And the stars flamed in the sunlight, for they were wrought of gems by Arwen daughter of Elrond; and the crown was bright in the morning, for it was wrought of mithril and gold. (5.6.57)
The "signs of Elendil" on this banner include the crown and the "Seven Stars." Of course, there is a real-life constellation with seven stars: the Pleiades, also known as the Seven Sisters. Could it be that the Pleiades gave Tolkien the idea for this image? Maybe. But The Lord of the Rings is also full of star symbolism that ties stars to both goodness in general, and elvishness in particular. Since Elendil's family line is supposed to be both good and close to the elves, it makes sense that stars are the symbols of Elendil's house.
Why do we associate the stars with elves and goodness? The elves frequently call to Gilthoniel and Elbereth, both of which are names for the Valar Queen of the Stars. Her very name is powerful enough to hurt the Nazgûl in The Fellowship of the Ring. And Eärendil's star, also known as the Morning and Evening Star, is supposed to give light to the Phial of Galadriel that Frodo and Sam use against Shelob in The Two Towers. Starlight is actually a weapon against evil in this series. Cool, huh?
Because of this general association between stars and the house of Elendil, the star symbol also becomes a useful way to indicate that someone is a descendant of Númenor (since Elendil is the last great man of Númenor). The Rangers who come to help Aragorn in his final battle against Sauron all wear cloaks "pinned upon the left shoulder by a brooch of silver shaped like a rayed star" (5.2.56). No, that doesn't mean they're part of Walker Texas Ranger's posse. It means they're all of Númenorean origin, and that means they're good news.